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Math Help - Confused About Drawing With X Intercepts

  1. #1
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    Exclamation Confused About Drawing With X Intercepts

    For each of the following:

    y= A ^ (x-2) - 3

    if A> 1

    domain:
    range:
    asymptote:

    Then Sketch.


    i got domain = all real
    range= y> -3 and asymptote -3.
    Im not sure if this is right though..
    and i need to draw a sketch of this..
    no idea how to. could some1 please explain how to do this.

    thanks.
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  2. #2
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    Quote Originally Posted by clp_53 View Post
    For each of the following:

    y= A ^ (x-2) - 3

    if A> 1

    ...
    i got domain = all real ....... OK
    range= y> -3 ....... OK
    and asymptote: y = -3. if x approaches negative infinity.
    Im not sure if this is right though..
    and i need to draw a sketch of this..
    no idea how to. could some1 please explain how to do this.

    thanks.
    All graphs of the family of functions pass through P(2, -2). (Why?)

    I've attached a sketch of the graphs of:

    y = \left(\frac32\right)^{x-2} - 3 and

    y = 2^{x-2} - 3 and

    y = 3^{x-2} - 3
    Attached Thumbnails Attached Thumbnails Confused About Drawing With X Intercepts-expfkt_schar.jpg  
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  3. #3
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    Hello, clp_53!

    y\:=\:A ^ {x-2} - 3\quad A> 1

    Find: the domain, range, and asymptote(s) ... then sketch.

    i got: . \begin{Bmatrix}\text{Domain:} & \text{all real x} \\\text{Range:} &  y \,>\, -3 \\\text{Asymptote:} & y = -3 \end{Bmatrix} . . . . Right!
    We're expected to know the graph of y \:=\:A^x,\;\;A > 1
    Code:
                              |       *
                              |
                              |      *
                              |     *
                              |   *
                              *
                        *     |
                 *            |
        *                     |
      - - - - - - - - - - - - + - - - - - -
                              |
    It has y-intercept (0,1).
    To the left, it approaches the x-axis.
    To the right, it soars upward.


    y \:=\:A^{x{\color{red}-2}} .is the same graph moved 2 units to the right.

    Then: . y \:=\:A^{x-2} \,{\color{red}-\, 3} .moves it 3 units down.

    Got it?

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